# ASCE 7-05 Sections 12.2.2 and 12.2.3: Combinations of seismic force-resisting systems

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It is rather common for different seismic force-resisting systems to be combined in the same building to resist the seismic forces. Two or more systems may be used such that there are horizontal combinations or vertical combinations, as shown in Figure 1 — on relatively rare occasions, there may be horizontal as well as vertical combinations in the same building.

Q: What R, Cd, and Ω0 values should be used in the design of the building when there is a combination of horizontal and/or vertical seismic force-resisting systems?

A: ASCE 7-05 Section 12.2.2 clearly states that for horizontal combinations of systems in different directions, the respective R, Cd, and Ω0 values are to be used.

ASCE 7-05 Section 12.2.3.2 sets forth R, Cd, and Ω0 values for when different systems are used in the same direction, but they do not form a dual system. Table 1 summarizes this section, and we included notes for situations not addressed by the code language.

ASCE 7-05 Section 12.2.3.1 sets a rule for vertical combinations of systems that the value of R used in the design of any story must be less than or equal to the value of R used in the given direction for the story above. Also, the values of Cd and Ω0 used in the design of any story must be greater than or equal to the values of Cd and Ω0 used in the given direction for the story above.

Figure 2 below illustrates how to properly select R, Cd, and Ω0 for a vertical combinations of seismic load-resisting systems. However, ASCE 7-05 makes three exceptions to this requirement for small rooftop structures; other supported, small structural systems; and detached one- or two-family dwellings of light-frame construction.

 Table 1: R, Cd, and Ω0 values are evaluated differently for horizontal combinations in the same direction. Figure 1: ASCE 7-05 provisions address how to properly select R, Cd, and Ω0 values when a combination of seismic force-resisting systems exists within the building.
 Figure 2: When evaluating verticalseismic force-resisting system combinations, R cannot increase as you go down and Cd and Ω0  cannot decrease as you go down.

S.K. Ghosh Associates Inc., is a structural seismic, and code consulting firm located in Palatine, Ill., and Aliso Viejo, Calif. President S.K. Ghosh, Ph.D., and Susan Dowty, S.E., are active in the development and interpretation of national structural code provisions. They can be contacted at skghosh@aol.com and susandowty@gmail.com, respectively, or at www.skghoshassociates.com